A Kiribati policeman named Toakai Teitoi was reportedly adrift at sea for 15 weeks, along with his brother-in-law, who succumbed to dehydration before rescue. Eventually, the man saw what seemed like an ill omen- a great white shark fin circling the boat. However, the shark did not attack. Instead, it nudged his boat until it got his attention, then swam off towards a fishing boat Teitoi would not have otherwise seen.

Quote that's in pretty much every article I can find on the subject:
“He was guiding me to a fishing boat. I looked up and there was a stern of a ship and I could see crew with binoculars looking at me.”

So, what do you think? Could a shark really have the intelligence to direct a man towards a fishing boat, or did it just investigate him, then go towards something that seemed more exciting? He claims it swam off after getting his attention, but I don't think he would have really seen its activities underwater.

Great whites often travel close enough to the surface that the man could have watched. I have trouble believing it would care enough to do this, as reported. It may have learned that when it bumps small boats, fish either fall off or are thrown off in appeasement. When the man's boat did not disgorge fish, it started swimming toward the other potential source of easy fish.

Shark experts frequently say that great whites are naturally curious animals. There's been a lot of debate about just how intelligent sharks are but they do show some definite learning ability: bull sharks in South Africa have learned to shadow fishing boats to steal fish after they've been hooked. Deliberately leading a man to safety, however, seems out of their cognitive abilities.

If the man was in a state of severe dehydration (as ATNM said, getting an actual link or two to the articles would be nice), it's quite likely that he wasn't entirely lucid and could have very easily misinterpreted what was happening.

That was my thought as well. For me, it's not so much a question of intelligence as it is of empathy. I find it hard to imagine a shark (or any fish, for that matter) with altruistic tendencies (Rhyme of the Chivalrous Shark notwithstanding).

He did say he'd started praying by this point. Maybe he believed the shark was sent/influenced by God, in which case the established science would be irrelevant to anyone inclined to believe in such miracles. I wouldn't be at all surprised if there were medieval stories of saints who were rescued or guided to safety by similar means.

(I mention this only as a possible insight into his reasoning on the subject. Obviously whether or not the idea has merit would be a subject of much disagreement.)

In any case, it might be safe to believe the shark did indeed "rescue" him in that it drew his attention to the fishing boat, even if it had no intention of doing so.